## The Flaw of Averages

The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

by Sam L. Savage

This is a book about how to manage in a world of uncertainty. The beginning section presents a number of statistical concepts in simplified language; more sophisticated techniques follow. The author discusses how these concepts apply in a wide variety of contexts including oil exploration, pharmaceutical R&D, the stock market, the housing bubble, weather, climate change, health care, gene pools, the war of terror, and supply chains. He also describes some illogical accounting rules required by the FASB and the SEC. Continue reading “The Flaw of Averages”

## Chance

Chance: A Guide to Gambling, Love, The Stock Market, and Just About Everything Else

By Amir D. Aczel (1950-2015)

This is a book about probability, the “quantitative measure of the likelihood of a given event.” The author applies probability theory in numerous scenarios.

Assuming a World War II pilot had a 2% chance of being shot down on each mission, what are the chances of a pilot being shot down in 50 missions?  Nope—it is not 50 x 0.02. Using the law of unions of independent events, the answer is 1 – 0.9850 = 64%.  In another example, there are three overnight couriers with an on-time record of 90%, 88%, and 92% respectively. If someone sent an important document using all three services, what is the probability of at least one of them delivering on time? The answer is 1 – (0.10 x 0.12 x 0.08) = 99.904%.

“So what have we noticed here? Continue reading “Chance”

## Innumeracy

Innumeracy: Mathematical Illiteracy and its Consequences

by John Allen Paulos

Innumeracy refers to mathematical incompetence. Given the frequency of misleading social media memes that simply don’t add up, I’d say the book is as relevant today as it was when published in 1988.

“If the headline reads that unemployment declined from 7.1 percent to 6.8 percent and doesn’t say that the confidence interval is plus or minus 1 percent, one might get the mistaken impression that something good happened. Given the sampling error, however, the ‘decline’ may be nonexistent, or there may even be an increase.” Continue reading “Innumeracy”